Photographs of the corona taken during the total eclipse of the sun, January 1, 1889 : structure of the corona

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692-

PHOTOGRAPHS OF THE COROiXA

TAKEN DURING THE

TOTAL ECLIPSE OF THE SUN,

JANUARY I, 1889.

STRUCTURE OF THE CORONA.

BY

DAVID P. TODD, Ph.D.,

Director Amherst College Observatory.

CITY OF WASHINGTON:
PUBLISHED BY THE SMITHSONIAN INSTITUTION.

1889.

The original of this book is in
the Cornell University Library.

There are no known copyright restrictions in
the United States on the use of the text.

http://www.archive.org/details/cu31924032176590

692-

PHOTOGRAPHS OF THE CORONA

TAKEN DURING THE

rn

TOTAL ECLIPSE OF THE SUN

JANUARY 1, 1889.

STRUCTURE OF THE CORONA.

DAVID P. TODD, Ph.D.

Director Amherst College Observatory.

CITY OF WASHINGTON:
PUBLISHED BY THE SMITHSONIAN INSTITUTION.

1889.
V

INTRODUCTORY NOTE.

The accompanying plates have been prepared from positive copies on glass of photo-
graphs of the total eclipse of the sun of January 1, 1889, kindly presented to the Smith-
sonian Institution by Professors Pickering, Holdcn, and Payne, Captain Floyd, General
Irish, and Mr. Burckhalter. The copies have, for tlie f^ake of comparison, been
reduced to a uniform diameter by Mr. Smillie, the photographer of the Institution, and
a descriptive note with remarks on the structure of the corona has been added at my
request by Professor Todd.

It is not intended to include these plates in the Contributions to Knowledge, but a
limited number of carefully prepared prints will be distributed to astronomers and others
specially interested in solar phy.sics.

S. P. LANGLEY,

Secretary.
Smithsonian Institution,

October 1, 1889.

(3)

ON THE STRUCTURE OF THE CORONA

AS INDICATED BY THE PHOTOGRAPHS TAKEN 1889, JANUARY 1.

By Professor David P. Todd.

On occasion of the eclipse of this date clear skies were everywhere prevalent.
A great variety of photographic apparatus was in the field and a rich harvest of
pictures was gathered.

At the request of Professor Langley, glass positives of all the better photo-
graphs were forwarded to the Smithsonian Institution for comparison and preser-
vation. These positives being contact prints, thei'e was, of course, great diversity
of scale, and the first step was to enlarge or reduce the photographs to conformity
with an arbitrary unit. For the unit of the moon's diameter Professor Langley
chose 25 millimeters, and the necessary negatives of this size were prepared by
Mr. Smillie, the photographer of the Institution. Prints from these secondary
negatives form Plate I. Of course the results would have been better had
all the original negatives been available. Captain Floyd alone transmitted an
original negative.

Also a series of lantern positives was prepared, and the photographs were
exhibited to the National Academy of Sciences on the 17th April, 1889. Certain
conclusions were drawn from the collation of the photographs, and suggestions
made for the observation of future eclipses. In the main these follow.

In the subjoined table are presented all the important circumstances and
conditions pertaining to these nine photographs of the corona. The top and
bottom of each print are north and south, and the right and left are west and
east, respectively. The sun's axis is inclined at an angle of between one and
two degrees with the north and south line (position angle = -I- 1°.4), and the
vertex or highest point of the sun and the trace of the ecliptic are shown with
sufficient accuracy for each figure by the diagram in Plate II.

(5)

6 STRUCTURE OF THE CORONA.

The excellence of Nos. 1 and 2 indicates the desirability of photographing
the corona with reflectors in the future.

In No. 3 the poor definition appears to be due partly to the lack of exact
focal adjustment and partly to the deficient clock-work, a temporary apparatus
having been devised for turning the polar axis by hand.

That a glass of less than two inches aperture and unadapted to photography
should have produced a photograph (No. 4) comparable with that obtained (No.
5) by a 13-inch objective specially corrected for the photographic rays is a matter
requiring minute investigation, and is suggestive as to eclipse outfits in the
future. There appear to be other effects than those due to difference of aperture
merely. Both these pictures are shown in Plate II of the size of the original
negatives.

In No. 8 the effect of the dry-plate granules is conspicuously brought
out by excessive enlargement. To a slight extent this is apparent in No. 9
also.

In commenting on this collection of photographs before the Academy, I ven-
tured the following observations :

(I) The axis of symmetry of the corona does not coincide with the axis of
revolution of the sun as determined from the solar spots. The corona aj^pears to
be at least a triple phenomenon* made up of —

(a) The polar rays, seen most prominently about the poles, but probably
extending into the equatorial regions, and not there seen because projected upon
the filaments which have their proper origin there.

{b) The inner equatorial corona, the lower regions of which bear some re-
semblance to an outer solar atmosphere, and have perhaps a closer connection
with truly solar phenomena than any other part.

(c) The outer equatorial corona, consisting of the long streamers, for the
most part visible only to the naked eye, and having perhaps no necessary con-
nection with the sun.

(II) The polar corona consists of rays, straight or nearly so, and radial from
neither the sun's centre nor the sun's poles. Rather they seem to radiate from
areas the centres of which are adjacent to the sun's poles ; and the law of their
inclination to the polar axis of the corona appears to be susceptible of precise
empirical determination.

A few of these rays appear to be double nearly their whole lenffth. For
the most part, if not entirely, the rays or beams have parallel sides. They can

* Note in this connection Young and Huggins on the compound spectrum of the cor.iiia, consisting of three
superposed spectra. Silliman's .lournal, vol. ll)2, p. 'iS, and Proc. lloyal Society, liilO, 18S'i, pa"-e 121.

STRUCTURE OF THE CORONA. i

be subdivided with increase of magnifying power, and are sharply defined like
the lines of the sun's spectrum. Between them the dark rifts sometimes extend
quite to the disk of the moon.

Occasionally a ray appears to have a slight curvature, in general from, but
often toward, the solar axis, and this may be due to optical or to photographic
illusion, or both.

(III) The inner equatorial corona emits a large percentage of the total light
of the corona. Photographs taken with clock-work show great detail in this
region, though the streamers are not generally so sharply defined as about the
poles. ^Many of these streamers appear to hare a real curvature.

Four large prominences are visible, two on each side of the sun and at about
35° of solar latitude, as if to suggest some connection between the protuberances
and the corona.

(IV) The equatorial streamers of the corona are for the most part lost
by the operation of enlargement. These streamers are very slightly curved,
while they are convergent on the east side of the sun and divergent on the west.

On the latter side and about 1° from the sun's centre there is a suggestion of
wider divergence, as if there were electric rei)ulsion between adjacent streamers,
as Huggins' theory would imply. The photographic evidence as to the existence
of a meteoritic ring or equatorial envelope surrounding the sun is inconclusive.

The fact of chief importance established appears to be the periodicity of the
outer corona in a cycle probably of equal duration with that of the solar spots.
A comparison of the corona of 1889 \vith those of 1867 (Cxrosch), 186S (Bullock ,
and 1878 (Langley, New^comb, and others) is sufficient to establish this periodicity
beyond reasonable doubt. The epoch of greatest extension of the equatorial
corona appears to coincide very nearly with the epoch of minimum sun spots.

(V) No rapid change in the structure of the corona can safely be inferred
from a comparison of photographs taken at the diflferent stations. The difi'er-
ences are slight, if any, and may well be due to diiferences of objectives, plates,
and development.

The time-difference between the photographs at Bartlett Springs and at Wil-
lows is about one minute. The only safe inference appears to be that, while the
corona mav change from hour to hour, there is no present indication of change
from minute to minute.

In order to investigate this question fully in the future, it will be necessary
to make two like series of exposures at widely separate stations, and combine
each series into an accurate representation of the entire corona, if possible, by
means of composite photography.

O STRUCTURE OF THE CORONA.

(VI) A few suggestions for the coming eclipse bearing on coronal structure
are pertinent. They are the more important as the decade of the nineties con-
tains only two eclipses likely to be well observed — 1893, April 16, in Brazil and
West Africa, and 1898, January 22, in East Africa and the west of India :

(1) For the minute study of the detailed structure of the corona it is abso-
lutely essential that the photographic telescope be equatorially mounted and
driven by perfect clock-work.

(2) These photographs should be taken on a scale as large as convenient in
order to avoid effects of the granulation of the dry-plate films.

(3) Means must be provided for the most accurate orientation of the polar
streamers. If a plumb-line or the parallel cannot be photographed on the plate,
exact orientation should be accomplished by optical measurement of the position
angle of a suitable prominence.

(4) Attention should be directed to photographing the outer coronal streamers
by the most delicate apparatus available.

(5) In view of differences in the photographic correction of objectives,
pairs of reflecting telescopes should be used, widely distant on the earth's surface,
and with identical plates. In \ie\\ of the greater absorption of the H K rays by
silver on glass, the reflector would preferably be made of speculum metal.

If dioptric instruments have to be used, the actinic focus for the coronal rays
should be experimentally determined with the greatest precison.

(6) Comparisons of different photographs and generalizations upon the
coronal structure are not worth attempting unless the precise I'elation of the solar
to the lunar centre is known. It is therefore essential that the exact time of the
middle of each exposure be known, together with the longitude and latitude of
the station within 15".

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-691

THE SOLAR CORONA,

DISCUSSED BY SPHERICAL HARMONICS.

BY

Peofessoe frank H. BIGELOW

CITY OF WASHINGTON:
PUBLISHED BY THE SillTHSOXIAN IXSTIirXIOX.

1889.

091

THE SOLAR CORONA,

DISCUSSED BY SPHERICAL HARMONICS.

BY

Professor FRANK H. BiaELOW.

CITY OF WASHINGTON:
PUBLISHED BY THE SMITHSONIAN IXSTITUTIOX,

1889.

JVDD ,t DETWEILEB, PRlyTEItS,
UASHIXOTON, D. C.

ADVERTISEMENT.

The following matliematical study of the wolar corona, as shown in the photographs
taken hy Messrs. Pickering and Barnard during the total ecli})se of January 1, 1889, is
sul^niitted to astronomers and physicists as a possible chu' to the explanation of the corona,
and as suggesting the direction to be taken in future oljservations and investigations.

The paper has Ik-cu recommended for publication by Professors Asaph Hall and
Cleveland Abbe, to whom it was referred in accordance with the usage of the Smith-
sonian Institution.

S. P. LANGLEY,

Secretary.

Smithsonian Institution,

Washington. October 1, 1889.

(B)

THE SOLAR CORONA,

DISCUSSED BY SPHERICAL HARMONICS.

Bv Professor Frank H. Bigelow.

The difficulty of analyzing the structure of the solar corona is increased by
the superposition of individual rays in projection on a plane perpendicular to the
line of sight. The polar streamers and the outline of the equatorial wings are
relatively free from this overlapping, and the body of the moon, in transit, cuts
off such rays over the disk as are most distorted, so that the problem ought to
be soluble by some theory applicable to the case of the rays specified

The structure to be accounted for consists : (1) of polar rays nearly vertical
at the coronal poles or axis of reference for the symmetrical figure, but inclining
more from, this axis than a radius vector to any point as the vectoral angle in-
creases ; (2) four wings disposed upon two axes, each inclined at an angle of
about 40° from the vertical; and (3) extensive equatorial wings seen more dis-
tinctly at periods of solar quiescence. This appearance upon a meridian section
must be translated into corresponding zones and sectors on the figure of revolu-
tion of the sun.

We propose to treat this subject by the theory of spherical harmonics, on
the supposition that we see a phenomenon similar to that of free electricity,
the rays being lines of force and the coronal matter being discharged from the
body of the sun, or arranged and controlled by these forces. In order to give the
solution a general foundation the important points of the theory of harmonics
specially relating to the case will be recapitulated, and the corresponding geo-
metrical solution will be given in a notation adapted to the sun. My references
are to Maxwell, Mascart and Joubert, Ferrer, Todhunter, Thomson and Tait
in their treatises on harmonics.

(5)

THE SOLAR CORONA.

THE HARMONIC THEORY.

Assume the centre of the sun's corona as the origin, the co-ordinate axes,
X, Y, Z, at any instant being the radius vector to the observer, that at right
angles, and the polar axis respectively. Take any set of secondary polar axes
distributed at will over the spherical surface, each axis, h^ h^, etc., being defined
as a definite direction from the origin, the cosines of the angles between these
axes being cos mi2, cos m^^, etc., in all combinations. Let any point in space
be defined as (r, Q)^ from axis Ai, (r, Q).^ from axis 7*^, etc. Then suppose there
are » axes, and that s is the number of cosines between them. Assume that a is
the number of poles of the n axes distributed uniformly on the equator from X at

distances — . From the point (r, 0) draw planes perpendicular one to each axis

(t

and successively differentiate the equation v = relatively to each pole.

It is known that La Place's equation, J^ + ^ J+ JJ^ = 0, is satisfied by a solid

harmonic of the degree i of the form H; = \i_ M; r' Y^ = r" + ^ V; .

In order that for a spherical closed surface the potential may satisfy the
equation continuously without becoming infinite at the origin or at infinity it is
converted into three terms :

Hi = ]± M; r' Yi within the sphere,

c = C Yj on the spherical surface,

V. = L-^' ^' without the sphere.

/pt -\- 1

These become, when expressed in terms of C :

£W_C /

2i + l ■ r' +^ ' '

wherein C is a constant and Y; is a surface harmonic. Y^ when expressed in the
general trigonometrical form is :

Y, = sum { (-ly }'i^_^ y{ cos e^- cos nf) j .

In case s = o, and consequently no poles are assumed symmetrically disposed
around the equator nor at random over the surface, but all are collected into one
pole, the surface harmonic becomes a zonal harmonic, whose form is :

Qi = sum„ \{-iy <,.,.-,'-* , . - (cos 0'-'^" sin B'"' ) \ ,

( ^ I'll \ji [_i — '2n ^ ' j

where n receives the values 0, 1, 2, 3, etc., for summation.

It is obvious, from the inspection of the symmetrical disposition of the corona,
that we deal with only one axis, and that therefore our harmonics are of the first
degree, i = I. Hence :

THE SOLAR CORONA.

Yi = Qi = 1 . COS ,
XT 4 //C

H, = — g— . r COS f) ,
= C . cos Q ,

Inside sphere.
Upon "
Outside "

3 r-

which upon differentiation satisfies the equation :

Hi _ ^ + 4 // (T = 0.
d r dr

THE geomi<:trical theory.

Let us now pass to the corresponding geometrical conditions. If we sup-
pose equal masses of potential of opposite signs, + in and — m, to be located on

4

the extremities of the polar axis, the moment is M = 2 R ??i = -g- 11 R^ C. The
equation for equipotential surfaces is v = M (— — '^) where r and r^ are the
distances from any point to the positive and negative poles respectively. (Fig. 1.)

8

THE SOLAR CORONA.

The equation of the lines of force is (cos d — cos 6^) = i — cos it = 2 //M
^vhere d and 0' are the angles between r and r, and the positive direction of the
axis, and « is the angle between the tangent to the line of force at the given point
and the polar axis. If ,5 and /S^ are the angles that this tangent makes with
r and r, then ^in /? sh^'" ^^^ ^^^ ^^^,^^ -^^^1^ is F = M I '-"^V + ~'4^ 1

If we suppose these potentials to be distributed ov^er the surrounding hemi-

spheres by the law of cosines, the surface density at any point is ^ = ; and if

these two masses instead of being distributed are brought infinitely netir together
at the centre of the sphere, so that = 0' and r = i\, then the equation of an

equipotential surface is v = M . '^^ , and the equation of a line of force is

N = 2 // M

sin^S

(1 — cos 11) =

N . 2 // sin^

r r '

where N is the order of the line taken, being proportional to the square root of
natural numbers. (Fig. 2.)

THE SOLAR CORONA. 9

To obtain the interior force, F;, let r cos = 1 in the expression for Hi ;

hence F; = — -g- n C, being directed opposite to the positive direction.

4
The moment, M= + — nC.rcos0

The interior potential, Hj = +-3-110 . r cos

The exterior potential, Vj = + 4 n C . R-' . ^!--

Resolving the exterior potential tangentially and normally to the circle
whose radius is r :

The tangential component, Fj = + -3- TI C . R' . ^-^ •

The normal component, F„ = + -g- TI C . R'^ . '^'^^, ■

Also resolving along the polar and equator axes :

The polar component, F^ = — |- n C . R^ (l-3cos^g) .

The equator component, F, = + -g- n C . R'' ^'"^3"°^ •

The whole mass of potential is m = n R^ . C, and the total flow of force, or
the quantity Q = (4 IT R') 11 C.

Now construct a diagram convenient for our purpose, in reference to the

corona, representing lines of equipotential and of force.

4 4 cos

In H, = -3- n C . r cos d, and Vi =-3- 11 C R' -^2 , we may regard the con-

COS

stants as unity ; hence Hi = r cos 6 and Vi = ^rr- In the interior of the sphere

the equipotential lines are parallel to the equator. Draw a spherical meridian
and divide the vertical radius into ten equal parts, each of which will represent
an equal diminution of potential in passing from the maximum at the poles to

zero at the equator. Outside the sphere compute r = -y|-y-" Conveniently we

assume for Vi the successive values 1.0, .9, .8, .7, .6, 0. and for cos B the

same in succession. A double-entry table will give us the values of r at the
angles 6 corresponding to the potential Vp

Plotting points on radii extended through the angles of equal difference of
cosines and connecting all j^oints for same Vi, we have a diagram of ovals sur-
rounding the poles becoming tangent to the equator at the centre of the sphere.

(A table of Equipotential Surfaces is given on the following page.)

10

THE SOLAR CORONA.

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O i-i w

THE SOLAR CORONA. U

The lines of force are constructed by the equation :

N = 2//(+ I //CR')^'f,

or, calling the constant n R'* C unity,

sin' tf . 8 //

N = o —

r 3

The successive integral numbers may be given to N, . 1 . 2 3, etc., and
the corresiDonding values of 6 computed. They are :

N=0 0=0 N=O0=O

1 20° 12'.7 5 00° 35.0

2 29 15.0 6 57 48 .(i

3 36 4.5 7 66 4.7

4 43 42.5 8 77 44.7

when we assume in the formula that r = 1. These give us the points at which
the lines of force of integral orders depart from the surface of the sphere. But
more conveniently for our purposes we may assign values to the angle 6, such
that the cosine of the successive angles differ by one-tenth radius, and compute
the values of N under this case :

U e = 25° 51' N = 1.593 If = 72 33 N = 7.624

36 52 3.016 78 28 8.043

45 34 4.272 84 15 8.294

53 8 5.362 87 8 8.357

60 6.283 90 8.378

66 25 7.037

To trace out the path of a line of force of any order N, take sin^ 6 ■

3r N

8 ri

assume the required N, assign successive values to r at convenient distances, and
compute 6 ; e. g. :

IfN = 1.593 andr

1

^ =

: 25.51

IfN = 1.593 andr =4

= 60.42

2

38. 4

5

77.10

3

49. 3

6

or assign values to Q and compute r.

(A table of Lines of Force is given on the following page.)

To find where the lines of any order N cut the. equator axis, take

3r N _
8 // -

assign the values to N and compute r

N= 1.539 r= 5.248 "
3.016 2.779

4.272 1.961

5.362 1.562

6.283 1.333

7.037 1.191

] or /

8 //

3N

N = 7.624

r = 1.099

8.043

1.042

8.294

1.010

8.357

1.002

8.378

1.000

12

THE SOLAR CORONA.

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THE SOLAR CORONA. 13

To find the order of line of force at the earth's mean distance from the sun,
talce the mean semi-diameter of the sun, 962", and the mean parallax of the
earth, 8".84S, and the earth is 108.7 radii of the sun distant from it. For
r = 109, N = 0.07686. The angular distance from the pole at which this line of
force leaves the sun is 5° 29' 47".

Graphically the lines of force cut the equipotential lines orthogonally, and
may be so drawn, starting at the points of the surface heretofore marked by
the equipotentials. These lines are ovals cutting the equator perpendicularly and
becoming tangent to the polar axis at the centre of the sphere. A test of the
accuracy of the drawing is found by taking the sides of any of the quadrilateral
figures, wherein the ratio of the mean distance between consecutive equipotential
surfaces is to the mean distance between consecutive lines of force as the half
the distance of the centre of the figure from the polar axis is to the unit of
measure.

APPLICATION TO THE CORONA.

An analysis of these lines of force appears to be a description of the visible
solar corona, and this analogy first suggested the explanation of the phenomena
now given. The concentration of potential at each pole throws lines vertical at
the polar region, bending gradually each side, and at a distance of 26° losing
one-tenth of the force, — the angle of the line of force to the polar axis bring
nearly 45° ; this curve closes on the equator at o.2o radii from the centre. The
next decimal line leaves the sphere at an angle of 67° to the vei'tical axis, and
having a potential of eight-tenths closes on the equator at 2.8 radii. The tliird
line of force is inclined at 76° to the axis, and having potential seven-tenths closes
on equator at 1.96 radii. The fourth line starts perpendicular to the vertical axis,
leaves the sun at jaolar distance 53°, closing on equator at 1.56 radii. The other
lines rapidly become more nearly parallel with the surface and close in as they
lose iDotential.

The solar corona can now be analyzed. The straight polar rays of high
tension carry the lightest substances, as hydrogen, meteoric matter, debris of
comets, and other coronal material, away from the sun, and they become soon
invisible by dispersion. Next we come to the strong quadrilateral rays of poten-
tial .9 .8 .7 .6, which united form the aj)pendages conspicuously seen at periods
of great solar activity. They rapidly diminish in intensity, and at the distance
of one radius have generally a potential of one to two tenths. The explanation
of the long equatorial wings, with absence of well-marked quadrilaterals, seen at
periods of minimum activity, is that they are due to the closing of the lines of
force about the equator. The re-entrance of these lines forms along the equator,

14 THE SOLAR CORONA.

the place of zero potential, a sort of pocket or receptacle wherein the coronal
matter is gradually carried by the forces, accumulated and retained as a solar
accompaniment. During periods of inactivity or low maximum potential the
streams along the region 40° — 60° polar distance diminish in intensity, so that
huge volumes are not carried away from the sui'face, but none the less what does
leave the sun is persistently transported to the equatorial plane of the corona.
In fact, the zodiacal light may be the accumulation at great distances from the
sun along this equator of such like material, being carried by forces, all of
which approach the equator perpendicularly, but there become zero. Here the
zodiacal coronal material has no way of escape, being once deposited.

We have a test of the accuracy of our theory which may be applied to
any portion of the coronal rays, using the caution that we deal with true rays
undisturbed by perspective and diffraction, and notably the polar and the outer
boundaries of the quadrilaterals are best available. From the centre of the sun,
with a radius vector r, draw a circle at any chosen point of such ray where the
curvature is well marked, and a tangent to the circle, prolonged to intercept the
polar axis with which it makes an angle. (See Fig. 2.) Let/ equal the angle at
which the line of force crosses this tangent ; draw another tangent to the line of
force and prolong it to the polar axis, then tan / = 2 cot = 3 tan X. The inter-
cept cut off from the centre of the sun by the force-tangent is one-third the inter-
cept cut of by the circle-tangent. I believe that this criterion holds good on
the photographs taken during recent eclipses, as the following readings show :
(A table of Readings is given on the opposite page.)

These readings were taken from Professor Holden's diagram (Monthly
Notices R. A. S., April, 1889) by centering one side of a right triangle on the
sun with radius 2 rotating to the several angles 6, previously selected to mark
the prominent rays, and reading the other side of the triangle on the axis ex-
tended and marked on a scale with the radius as unit. Finally an edge was laid
on the local lines at (rO), and the reading on the axis again taken. It must be
clearly kept in mind that it is not the direction of the whole ray from its base on
the sun to the point (r 0), but the direction tangent to the ray at the point (r 0).
Besides the local inaccuracies there may be a slight error in placing the direc-
tion of the axes, and the readings in the S. E. quadrant suggest this pi'esump-
tion. Still the approximation of the ratio U> 3.0 is so evident as to show the
application of this theory to the solar corona and also to witness the fidelity of
Professor Holden's drawing.

I have just had the pleasure of seeing one of the photographs of the inner
corona and one of the outer taken by the Harvard College party Januarv 1,
1889, and the details are shown so clearly that our theory is at once able to be

THE SOLAR CORONA.

READINGS ON HOLDEN'S DIAGRAM.

15

Radius Angle Intercepts by-

"'• Circle-Tangent. Force- Tangent.

N. W. Quadrant-

N. E. Quadrant.

S. W. Quadrant-

S. E. Quadrant-

s'"
16
22
29
35
47

3°
10
16
18
23
28
36
53
64
72

2.01
2.07
2.15
2.26
2.42
2.83

2.00
2.03
2.07
2.09
2.13
2.26
2.4.3
3.32
4.62
6.70

3°

2.00

6

2.02

11

2.04

19

2.11

41

2.62

50

3.07

56

3.60

6°

2.02

12

2.04

19

2.10

41

2.59

51

3.08

56

3.60

.65
.66
.71
.50
.59
.85

.65
.72

. ( o

.72
.75
.74

. 77

1.07
1..35
1.20

.50

.55
.•58
.70
.84
1.02
1.21

.61
.57
.60
.72
.90
1.20

Ratio.

3.09
3.14
3.03
4.51
I 4.10
3.32
3.20

3,08
2.82
2.83
2.96
2.83
3.01
3.18
3.10
3.45

15^58 1

2.97

4.00
3.67
^53
8.01
3.12
■3.01
2.97
3.03

3.32
3.-52
3.50
3.59
3.42
3.00
3.39

Local curvature too straight.

Mean.

Local curvature faulty.

Mean.

Local lines in error.

Mean.

Whole Quadrant may need
adjustment as to its axis.

Mean.

The necessity is obvious of rejecting freely such lines of force as are not natural, and the difficulty of obtaining
true lines is at present great.

16

THE SOLAE CORONA.

tested. I give a table of the measures whea our rule of polar intercepts is ap-
plied to tlie ray structure. They can be verified by any one possessing a Pickering
photograph on celluloid.

THE PICKERING PHOTOGRAPHS.
THE INNER CORONA.

^i"

^' bfs

Kadius ?.
Angle 9-

O <D

C) t^ G

1— 1

^ S3

a."

t-, ^ ^
'^ o c

c
1 ad rant.

a,

CD

N. W. Quadrant.

CD
O

u

C
M

c

P.
<v

CD
U

B

M

^2
Quadrant.

N. E. Q

s. w.

Quadrant.

S, E.

1.00 5°

1,00

0.33

3.03

0.33

3.03

0.31

3.02

0.32

1
3.01

10°
15°

1.01
1.03

0.34
0.38

2.97
2.70

0.34
0.38

2.97
2.70

0.33

3.01
2.34

0.34
0.40

2.97
2.58

0.44

20°

1.05

0.40

2.63

0.71

1.50

0.49

2.14

0.45

2.33

25°
30°

1.10
1.16

0.39
0.42

2.84
2.76

0.67
0.58

1.64
2.00

0.51
0.50

2.16
2.82

0.42

2.62
2.79

0.42

35°
40°
45°

1.22
1.31
1.42

0.42
0.46
0.48

2.90
2.85
2.96

0.54 .
0,51 !

2.26
2.57
2.84

0,.52

2.35
2.73
2.89

0.43
0.45
0.48

2.84
2.91
2.96

0.48
0.49

0.50

50°

1.56

0.53

2.94

0.56

2,79

0.51

3,01

52

3.00

5fl°

1.74

0.58

3.00

0.58

3.00

0.58

3.00

0.56

3.01

60°

2.00

0.68

2.94

2.88

2.89

2.94

--

2.94

THE

; OUTER

COR

ONA.

1.20 5°

1.21

0.40 '

3.00

0.41

2.95

0.43

2,81

0.41

2.95

10°

1.22

0.42

2.90

0.42

2.90

0.67

1,97

0.42

2.90

15°

1.24

0.43

2.87

0.44

2.84

0.62

2.00

0.42

2.95

20°

1.28

0.44

2.90

0.63

2.00

0.63

2.00

0.45

2.84

25°

1.32

0.45

2.93

0.64

2.01

0.58

o .js

0.06

2.00

30°

1.39

0.47

2.96

0.65

2.29

0.54

2.39

0.68

2.00

85°

1.47

0.50

2.94

0,63

2,33

0.55

2.67

O.o;!

2.33

40°

1.57

0.53

2.9li

0.51

2.91

O.r.5

2.41

45°

1.70

0.56

3.00

0.57

2.9S

0.60

2,83

50°

1.87

0.60

3.01

0.61

3.07

55°

I'.O'.i

0.67

3.01

2,95

2,90

----

2.94

----

2.89

Bracketed intercepts omitted in taking mean? ; 55 readings retained ; 27 show distortion.

Note.— It is evident that the efFeot of projection of the lines of spherical harmonics on a plane is to flatten them, so that the
force- tangent becomes elevated at its intercept on the polar axis. Hence the readings of this factor are too large, and the value of
the ratio too small, by an amount depending upon the error of the curves in projection.

THE SOLAR CORONA. 17

A scale was constructed as follows to facilitate the measurement of the lines on
the photographs : A positive on glass, showing tine lines on a transparent field, was
made from a drawing, which consists of concentric circles, the first coinciding with
the sun's disk, the others expanding by tenths of a radius to the distance of three
radii ; also a series of radii at five degrees apart. The polar axis was subdivided and
marked in figures, and the radii were numbered. This was reduced to the size
of the picture to be discussed, and the celluloid photograph being laid against
the scale and backed by a plate of glass formed a transparency which, viewed
against bright sky light, rendered the direction of the rays very distinct. (See
Plate I.) The circle-tangent intercept readings were taken from a table of secants :
the force-tangent intercepts were read from the picture by laying an ivory scale on
the ray in question. Some practice and judgment were required to distinguish
true and false directions, but considerable uniformity was acquired in the way
of independent measures.

An inspection of the table for the inner and the outer corona shows a decided
determination of the constant ratio 3.00. In the N. E. quadrant for both coronas
there is hardly a divergence from it ; in the N. W. quadrant between 20° and
40° there is a sharp change indicating some disturbance at this place ; the S. W-
quadrant shows a similar confusion ; and the S. E. is again quite regular. Some
solar currents seem to have swept the poles and the rays on the western side of
the sun.

It may be mentioned that these readings are for individual pictures and
with poles selected by best judgment. A comparison of many pictures taken at
ditferent times and with various kinds of apparatus under the assumption that
our constant 3.00 is a fundamental ratio may lead to valuable deductions as to
the coronal forces. In this connection the solar prominences and the fibres of
the chromosphere should be compared with the direction of the lines of force as
they leave the solar surface.

It is hoiked that future eclipses may furnish us with pictures of the corona
so clear that the measures may be made with certainty.

It is plain that the accuracy of the results depends upon our ability to locate
the polar axes. The general radiation at the poles shows the approximate posi-
tion, and the radial ray is probably near the vertex, but if our rule is granted as
true for the corona it becomes a means of fixing the pole precisely, referred to
the whole structure of a hemisphere, rather than leaving us to depend upon ap-
pearances of rays, which probably undergo a certain amount of local variation.

The assumption regarding the poles of the corona has usually been that they
are in a diametral line passing through the centre of the sun. Upon applying
the principle just stated to the southern vertex, at first assuming that it lay on

18

THE SOLAR CORONA.

SOLAR CORONA.— BiGELOW.

Plate I.

Diagram oi'- Scale p'oi

Intkkckpt Readings.

THE SOLAR CORONA. 19

the same diameter as the northern, I found that my intercept ratios were imtrue.
However, on taking the vertex in the southwestern quadrant at 169° from the
northern, the readings were rectified.

We have avoided speaking of the apparent coronal structure as a phenom-
enon of electricity in deference to the doubt that free electricity can exist at such
high temperatures as prevail on the sun's surface, but have shown that some
force is present acting upon the corona according to the laws of electric potential.
An inverse argument might at once be drawn from this applicability of the for-
mulae of statical electricity to the coronal structure that a form of energy analo-
gous to electricity exists on the surface of the sun, but we need not insist upon
the name of the active repulsive force whose potential we are discussing.

The value of the potential at any point of a line of force can be easily com-
puted, but a diagram plotted in tenths-potentials renders the work very simple.
Referring again to the Holden drawing, and for the present calling C equal to
unity, we may estimate the value of the potential at the edges of the corona as
recorded by the photograph.

At the north pole the rays extend to potential

0.35
0.50
0.15
0.10
0.20
0.15

At the south pole the rays extend to potential

At the northwest quadrilateral the rays extend to potential

At the southwest quadrilateral the rays extend to potential

At the northeast quadrilateral the rays extend to potential

At the southeast quadrilateral the rays extend to potential

Remembering that the smaller the potential the greater the distance seen
from the edge of the sun, we note that the western quadrilaterals are generally
longer, extending about one and one-third radii from the sun. They are sym-
metrically disposed to the poles assigned by our formula, the axis of symmetry
lying 85° from the north to the west. The northeast quadrilateral is shorter for
the same reason, and the tendency is to make the larger amount of matter visible
in the 169° side of the axis. The diminution of matter along the axis of sym-
metry is very obvious. At certain parts of the quadrilateral the curvature of
the rays is marked and in the right direction .

I had the diagram transferred to a transparent positive photograph scale
reduced to the solar diameter, upon which the mounting was made, as above
described, for the measure. It was seen at a glance, by counting the value of the
lines, to what potential the matter attaching to any line of force was visible. On
the same scale were produced the lines of force at the decimal potentials, and an
inspection of the curvature of the computed lines and the coronal lines, when
superposed, is sufficient to substantiate the truth of the theory. (See Plate II.)
It is seen also that a field of accurate and intelligent study of the solar forces
is now opened, and that the coronal pictures which show true structure become
valuable.

20

THE SOLAR CORONA.

SOLAR CORONA.— BiGELow.

Plate II.

Diagram oj-' Lines op Fukc'e,
(Upper part.)

DiAGKAM OK EqUIPOTENTIAL SuEFACES.

(Lower part.)

THE SOLAR CORONA. 21

TEREESTPJAL MAUNETLS^f.

In treating the problem of the earth's magnetism it has been generally sup-
posed that the forces of induction from the sun to the earth are in straight lines
following the vector joining these bodies. We now see that the earth lies in a mag-
netic tield, uniform by reason of its distance from the sun, the lines of force
being directed nearly perpendicular to the plane of the earth's orbit instead of
parallel to it, and of low potential, as the formula shows that the earth lies near
the plane of the equator of the corona. It is not yet known exactly what rela-
tion the polar axis of the corona holds to the axis of revolution of the sun, or to
the true N. and S., but it may be determined by a study of the coronal lines,
[f it should appear that the angle is considerable between the j)lane of the coronal
equator and the ecliptic, even supposing the corona does not oscillate, yet the
earth in its orbit must be passing through fields variable in potential and direc-
tion, which will condition some of the periodic changes of the terrestrial mag.
netism. Knowing the potential of the earth's magnetism and its variations the
data ought to be accessible for obtaining the solar constant of maximum super-
ficial density of electricity, and thus give a clue to the forces acting within the
sun.

With the data at present available it is difficult to assign the position of the
coronal pole to its true place on the solar surface, and the pictures heretofore ob-
tained, which deal almost exclusively with the general outline of the corona instead
of with the direction of the rifts and structural lines, afford little ground for
deduction from symmetrical forms. If we suppose the poles of the ecliptic, the
sun and the corona to be in the plane of vision the relative places are 6°.o from
pole of ecliptic to the pole of the sun and probably 12°. 5 to the pole of the
corona. One rotation of the sun on its axis will then cause the coronal equator
to range from about 13° north to 0° on the ecliptic. If Vj is the maximum po-
tential at the pole of the corona on the surface of the sun the corresponding-
potentials at the mean distance of the earth, 108 solar radii, are :

r = 108, e = 75°, Vb = 0.0000222 = ^j^^.

V

80° 0.0000149 -QT^ooo •

85° 0.0000075
90° 0.0000000

V,

133.000-

If the corona follows the rotation of the pole the effect is to draw the lines
of force up and down, north and south, in the region of the earth, so that it lies

22 THE SOLAR CORONA.

V
in potentials continuously changing from zero to 45^^ in a period of 26.33 days.

At the same time the earth's orbital motion causes it to cut them into forces of
induction, which would tend to make variations in the earth's magnetism. It is
obvious that the general view is sustained that the direct magnetic influences
from the sun are very slight, yet Hornstein's period should show variations con-
firming these coronal changes, and if the final residual of the earth's magnetic
variations can be completely assorted we should have from the coronal period a
means of fixing the polar positions, and also the ratio of the solar potential to
that of the earth's magnetism.

arY610 *^™" ""'"""^ Ubrary

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